Usually you would get a smart strip, but I am unsure it would work with a laptop brick.
Sleep is not a good option as most on board devices (lan, USB and sometimes video has a tendency to not work properly), and you might want to invoke a hard drive power down and if your laptop supports it, wake from LAN. I know my ASUS FCS3 with the IBM chipset dies when it hibernates and nothing seems to work properly unless you reboot.
I like cheap android phones and tablets - the crap ones with low memory and processor speeds, as they work as great interfaces to PCs. You can remote connect the PC and Projector via this method. You might want to do some research on this.
Other than that you could look at wireless power sockets. I noticed a generic at Wallymart and they have the same at ASDA depending on your geographic location. They work well. Not cheap but, it never is in this hobby.